If four identical resistors, of resistance 8 ohm, are first connected in series so as to give an eff

Question

If four identical resistors, of resistance 8 ohm, are first connected in series so as to give an effective resistance $R_{s}$, and then connected in parallel so as to give an effective resistance $R_{p}$, then the ratio $\frac{R_{s}}{R_{p}}$ is\

Professor PC Thomas Classes · Answer

(d): Given that, $R_{1}=R_{2}=R_{3}=R_{4}=8 \Omega$ For series combination of the given resistors, $$ R_{S}=R_{1}+R_{2}+R_{3}+R_{4}=(8+8+8+8) \Omega=32 \Omega $$ For parallel combination of the given resistors, $$ \begin{aligned} & \frac{1}{R_{P}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}+\frac{1}{R_{4}}=\left(\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}ight) \Omega=\frac{1}{2} \Omega \ \Rightarrow & R_{P}=2 \Omega \ 	herefore & \frac{R_{S}}{R_{P}}=\frac{32}{2}=16 \end{aligned} $$